In this paper we study the neutrosophic triplet groups for a ∈ Z2p and prove this collection of triplets (a, neut(a), anti(a)) if trivial forms a semigroup under product, and semi-neutrosophic triplets are included in that collection. Otherwise, they form a group under product, and it is of order (p - 1), with (p + 1, p + 1, p + 1) as the multiplicative identity. The new notion of pseudo primitive element is introduced in Z2p analogous to primitive elements in Zp, where p is a prime. Open problems based on the pseudo primitive elements are proposed. Here, we restrict our study to Z2p and take only the usual product modulo 2p. © 2018 by the authors.